A274149 - OEIS

A274149

Number of integers in n-th generation of tree T(-1/4) defined in Comments.

1, 1, 1, 1, 1, 2, 2, 3, 4, 6, 7, 9, 12, 17, 22, 29, 38, 51, 68, 90, 119, 158, 209, 277, 368, 489, 648, 858, 1137, 1509, 2002, 2655, 3520, 4667, 6189, 8208, 10885, 14436, 19141, 25382, 33659, 44638, 59195, 78497, 104092, 138036, 183050, 242745, 321904, 426875

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,6

COMMENTS

Let T* be the infinite tree with root 0 generated by these rules: if p is in T*, then p+1 is in T* and x*p is in T*. Let g(n) be the set of nodes in the n-th generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc. Let T(r) be the tree obtained by substituting r for x.

See A274142 for a guide to related sequences.

LINKS

Kenny Lau, Table of n, a(n) for n = 0..8153

FORMULA

a(n-1) = length of row n of the array in A274185.

EXAMPLE

For r = -1/4, we have g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.

MATHEMATICA

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];

u = Table[t[[k]] /. x -> -1/4, {k, 1, z}];

Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

CROSSREFS